SAT Math Multiple Choice Practice Question 210: Answer and Explanation

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Question: 210

12. Given that the following statement is true, which statement is necessarily also true?

If Mary is at work, then Pierre is having lunch.

A. Mary is at work.
B. If Pierre is having lunch, then Mary is at work.
C. If Mary is not at work, then Pierre is not having lunch.
D. If Pierre is not having lunch, then Mary is at work.
E. If Pierre is not having lunch, then Mary is not at work.

Correct Answer: E

Explanation:

E. The thing you need to know to solve problems like this is that if you're given an if-then statement, the only other thing that you know is true is the contrapositive of that statement. Say you have the statement "If I study with SAT For Dummies, then I ace the SAT." The contrapositive of that statement is "If I don't ace the SAT, then I didn't study with SAT For Dummies." The contrapositive switches the order of the original if-then statement and makes the individual parts of the statement have the opposite meaning. If an if-then statement is true, then its contrapositive is automatically also true. So, the contrapositive of "If Mary is at work, then Pierre is having lunch" is "If Pierre is not having lunch, then Mary is not at work."

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